BAYESIAN PARAMETER ESTIMATION OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN IRAQI EXCHANGE PARALLEL MARKET

This paper discussed the Bayesian theory for estimating the parameter of delay in both functions of the drift term and volatility term in the linear stochastic delay differential equations (SDDE). The explicit solution usually is hard to find for this type of stochastic differential equation and Euler-Maruyama method are more likely used in literature reviews as numerical technique to find the parameter estimates. We employed different priors distributions for deriving the posterior distributions with Gibbs sampler algorithm and Metropolis-Hastings algorithm. Also, we applied the Bayesian analysis to discuss the impact of the delay parameter estimates in the parallel currency-exchange market of dollar in the Iraqi. Deviance information criterion (DIC) used to compare the results of SDDE with Geometric Brownian Motion (GBM). The results of Bayesian estimation shows that can SDDE has the less value of DIC which indicates the SDDE have the more ability for studying the behavior of Iraqi parallel currency-exchange market than (GBM).